The Floquet theory of the periodic Euler-Bernoulli equation
The spectrum of the eigenvalue problem \[ \bigl[a(x)u''(x)\bigr]''=\lambda\rho(x)u(x),\;-\infty<x<\infty,\tag{1} \] is studied. Here, the functions \(a(x)\) and \(\rho(x)\) are strictly positive and periodic with common period. The equality between algebraic and geometric multiplicities of the periodic and antiperiodic eigenvalues is proved. The equation (1) models transverse vibrations of a thin straight beam.
scientific article; zbMATH DE number 1241034
scientific article